Question

A​ $5000, 14.5% bond with​ semi-annual coupons redeemable at par on August​ 1, 2022, was purchased on March​ 5, 2011, at 95.5. What was the approximate yield​ rate?

The approximate yield rate was ​%.

​(Round the final answer to four decimal places as needed. Round all intermediate values to four decimal places as​ needed.)

Answer 1

Face Value, F = $ 5,000

Price, P = $ 95.5

Coupon Rate = 14.5 %

Semi-annual coupon rate = 14.5 % / 2 = 7.25 %

Coupon Payment, C = 7.25 % off $ 5000 = $ 362.5

Issue Date = March 5 2011

Redemption Date = August 1 2022

No. of years = 11 years 146 days

No. of semi-annual periods = ( 11 * 2 ) + ( 146 / 182 ) = 22 + 0.8022 = 22.8022

Note: 146 days is 0.8022 of a semi-annual period ( 365 / 2 = 182 days )

Now,

Approximate Yield = [ C + { ( F - P ) / n } ] / [ (F + P) / 2 ]

= [ 362.5 + { (5000 - 95.5) / 22.8022 } ] / [ (5000 + 95.5) / 2 ]

= 22.6705 %

Since, the above yield to maturity is for semi-annual period, we need to convert it for annual periods.

Hence, Approximate yield = 22.6705 % * 2 = 45.3411 % [ this is an approximate yield as solved on pen and paper]

As per the excel calculations, the exact yield rate is 42.4642 %